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<h1>VMT_Vorticity
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>Not currently implemented</strong></div>

<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>function [V] = VMT_Vorticity(V) </strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre class="comment"> Not currently implemented

 Computes normalized STREAMWISE vorticity for the averaged cross-section
 based 3 different measures of secondary flow (Transverse (v), Secondary
 (zsd), Secondary (Roz)). This function uses the smoothed values of each
 component, and thus is called with each REPLOT.
 
 Vorticity (\omega) is normalized by the channel top width &amp;
 average streamwise velocity:
       \omega = \tilde{\omega} frac{B}{U} 
 
 FROM WIKIPEDIA: In fluid dynamics, the vorticity is a vector that
 describes the local spinning motion of a fluid near some point, as would
 be seen by an observer located at that point and traveling along with the
 fluid. Conceptually, the vorticity could be determined by marking the
 particles of the fluid in a small neighborhood of the point in question,
 and watching their relative displacements as they move along the flow.
 The vorticity vector would be twice the mean angular velocity vector of
 those particles relative to their center of mass, oriented according to
 the right-hand rule. This quantity must not be confused with the angular
 velocity of the particles relative to some other point. More precisely,
 the vorticity of a flow is a vector field (\omega), equal to the CURL
 (rotational) of its velocity field (v,w).
 
 Written by Frank L. Engel, USGS
 Last modified: F.L. Engel, USGS, 12/21/2012</pre></div>

<!-- crossreference -->
<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../matlabicon.gif)">
</ul>
This function is called by:
<ul style="list-style-image:url(../matlabicon.gif)">
</ul>
<!-- crossreference -->



<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [V] = VMT_Vorticity(V)</a>
0002 <span class="comment">% Not currently implemented</span>
0003 <span class="comment">%</span>
0004 <span class="comment">% Computes normalized STREAMWISE vorticity for the averaged cross-section</span>
0005 <span class="comment">% based 3 different measures of secondary flow (Transverse (v), Secondary</span>
0006 <span class="comment">% (zsd), Secondary (Roz)). This function uses the smoothed values of each</span>
0007 <span class="comment">% component, and thus is called with each REPLOT.</span>
0008 <span class="comment">%</span>
0009 <span class="comment">% Vorticity (\omega) is normalized by the channel top width &amp;</span>
0010 <span class="comment">% average streamwise velocity:</span>
0011 <span class="comment">%       \omega = \tilde{\omega} frac{B}{U}</span>
0012 <span class="comment">%</span>
0013 <span class="comment">% FROM WIKIPEDIA: In fluid dynamics, the vorticity is a vector that</span>
0014 <span class="comment">% describes the local spinning motion of a fluid near some point, as would</span>
0015 <span class="comment">% be seen by an observer located at that point and traveling along with the</span>
0016 <span class="comment">% fluid. Conceptually, the vorticity could be determined by marking the</span>
0017 <span class="comment">% particles of the fluid in a small neighborhood of the point in question,</span>
0018 <span class="comment">% and watching their relative displacements as they move along the flow.</span>
0019 <span class="comment">% The vorticity vector would be twice the mean angular velocity vector of</span>
0020 <span class="comment">% those particles relative to their center of mass, oriented according to</span>
0021 <span class="comment">% the right-hand rule. This quantity must not be confused with the angular</span>
0022 <span class="comment">% velocity of the particles relative to some other point. More precisely,</span>
0023 <span class="comment">% the vorticity of a flow is a vector field (\omega), equal to the CURL</span>
0024 <span class="comment">% (rotational) of its velocity field (v,w).</span>
0025 <span class="comment">%</span>
0026 <span class="comment">% Written by Frank L. Engel, USGS</span>
0027 <span class="comment">% Last modified: F.L. Engel, USGS, 12/21/2012</span>
0028 
0029 <span class="comment">% Begin code</span>
0030 
0031 B = V.dl;
0032 U = nanmean(V.u(:));
0033 
0034 [V.vorticity_vw,~]= curl(<span class="keyword">...</span>
0035     V.mcsDist,<span class="keyword">...</span>
0036     V.mcsDepth,<span class="keyword">...</span>
0037     V.vSmooth,<span class="keyword">...</span>
0038     V.wSmooth);
0039 V.vorticity_vw = -V.vorticity_vw.*B./U; <span class="comment">% reverse sign to keep RH coordinates</span>
0040 
0041 [V.vorticity_zsd,~]= curl(<span class="keyword">...</span>
0042     V.mcsDist,<span class="keyword">...</span>
0043     V.mcsDepth,<span class="keyword">...</span>
0044     V.vsSmooth,<span class="keyword">...</span>
0045     V.wSmooth);
0046 V.vorticity_zsd = -V.vorticity_zsd.*B./U;
0047 
0048 [V.vorticity_roz,~]= curl(<span class="keyword">...</span>
0049     V.mcsDist,<span class="keyword">...</span>
0050     V.mcsDepth,<span class="keyword">...</span>
0051     V.Roz.usSmooth,<span class="keyword">...</span>
0052     V.wSmooth);
0053 V.vorticity_roz = -V.vorticity_roz.*B./U;
0054 
0055 <span class="comment">% Vertical vorticity -- not saved in V struct, experiemental only</span>
0056 [vorticity_uv,~]= curl(<span class="keyword">...</span>
0057     V.mcsDist,<span class="keyword">...</span>
0058     V.mcsDepth,<span class="keyword">...</span>
0059     V.uSmooth,<span class="keyword">...</span>
0060     V.vSmooth);
0061 vorticity_uv = -vorticity_uv.*B./U; <span class="comment">% reverse sign to keep RH coordinates</span></pre></div>
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